MATH 30-1

1.1 Horizontal and Vertical Translations

Horizontal Translation of x² graph

y = (x - a)²

• If a < 0 (negative) the graph slides right.
• a = 0 is the normal position (default).
• If a > 0 (positive) the graph slides left.

1.2 Reflections and Stretches

Function Transformation Horizontal stretch of x² graph

y = a x²

• If a < 1 the graph gets wider.
• a = 1 is the normal size (default).
• If a > 1 the graph gets narrower.

Function Transformation Vertical stretch of x² graph

y = a x²

• If a < 1 the graph gets shorter.
• a = 1 is the normal size (default).
• If a > 1 the graph gets taller.

Function Vertical Reflection 1

y = - |x|
Every point is reflected in the x-axis. If the original has y value of 5 the reflected point has a y value of -5.
Point on the x axis don't move when reflected.

Function reflection in X axis with 2 invariant points

Point on the x axis don't move when a graph is reflected in the x-axis.

1.3 Combining Transformations

1.4 Inverse of a Relation

Inverse of a Linear Function Reflection in xy


Inverse of a Square Function (parabola) Reflection in xy

3.1 Characteristics of Polynomial Functions

3 1 Characteristics of Polynomial Functions

3.2 The Remainder Theorem

3.2 Remainder Theorem

3.3 The Factor Theorem